NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 are the part of NCERT Solutions for Class 7 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 (Rationalised Contents)

Ex 5.2 Class 7 Maths Question 1.

State the property that is used in each of the following statements?

(i) If a || b, then
∠1 = ∠5
(ii) If ∠4 = ∠6, then a || b
(iii) If ∠4 + ∠5 = 180°, then a || b

Solution:
(i) We have a || b
∴ ∠1 = ∠5

Property used: If two lines are parallel and cut by a transversal, then the pairs of corresponding angles are equal.

(ii) We have ∠4 = ∠6
∴ a || b

Property used: If a pair of alternate angles are equal, then the lines are parallel.

(iii) We have ∠4 + ∠5 = 180°
∴ a || b

Property used: If the sum of the co-interior angles is 180°, then the lines are parallel.

Ex 5.2 Class 7 Maths Question 2.

In the given figure, identify

(i) the pairs of corresponding angles.
(ii) the pairs of alternate interior angles.
(iii) the pairs of interior angles on the same side of the transversal.

(iv) the vertically opposite angles.

Solution:
(i) The pairs of corresponding angles are: ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7.
(ii) The pairs of alternate interior angles are: ∠2 and ∠8, ∠3 and ∠5.
(iii) The pairs of interior angles on the same side of the transversal are: ∠2 and ∠5, ∠3 and ∠8.

(iv) The vertically opposite angles are: ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8.

Ex 5.2 Class 7 Maths Question 3.

In the given figure, p || q. Find the unknown angles.

Solution:
∠e + 125° = 180°         (Linear pair of angles)
∴ ∠e = 180° – 125° = 55°
∠e = ∠f                         (Vertically opposite angles)
∴ ∠f = 55°
∠a = ∠f = 55°            (Alternate interior angles)
∠c = ∠a = 55°            (Vertically opposite angles)
∠d = 125°                  (Corresponding angles)
∠b = ∠d = 125°         (Vertically opposite angles)
Thus, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠d = 125°, ∠e = 55°, ∠f = 55°.

Ex 5.2 Class 7 Maths Question 4.

Find the value of x in each of the following figures, if l || m.

Solution:
(i) Let the vertically opposite angle of 110° be y.
∴ y = 110°             (Vertically opposite angles)
∠x + ∠y = 180°     (Sum of interior angle on the same side of transversal)
∠x + 110° = 180° .
∴ ∠x = 180° – 110° = 70°
Thus, x = 70°
(ii) ∠x = 100°        (Pair of corresponding angles)

Ex 5.2 Class 7 Maths Question 5.

In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find
(i) ∠DGC
(ii) ∠DEF

Solution:
Given: AB || DE and BC || EF
∠ABC = 70°
(i) ∠DGC = ∠ABC (Pair of corresponding angles)
∠DGC = 70°
(ii) ∠DEF = ∠DGC
∠DEF = 70° (Pair of corresponding angles)

Ex 5.2 Class 7 Maths Question 6.

In the given figure below, decide whether l is parallel to m.

Solution:
(i) The sum of the interior angles on the same side of transversal
= 126° + 44° = 170° ≠ 180°
∴ l is not parallel to m.

(ii) Let the angle opposite to 75° be x.
x = 75° (Vertically opposite angles)
∴ The sum of the interior angles on the same side of transversal
= x + 75° = 75° + 75° = 150° ≠ 180°
∴ l is not parallel to m.

(iii) Let the angle opposite to 57° be y.
∴ ∠y = 57° (Vertically opposite angles)
∴ The sum of the interior angles on the same side of transversal
= 57° + 123° = 180°
∴ l is parallel to m.

(iv) Let the angle opposite to 72° be z.
∴ z = 70° (Vertically opposite angles)
∴ The sum of the interior angles on the same side of transversal
= z + 98° = 72° + 98° = 170° ≠ 180°
∴ l is not parallel to m.